115 LearnersLast updated on May 26th, 2025
Cube Root of 15625
A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 15625 and explain the methods used.
What is the Cube Root of 15625?
We have learned the definition of the cube root. Now, let’s learn how it is represented using a symbol and exponent. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓. In exponential form, ∛15625 is written as 15625(1/3).
The cube root is just the opposite operation of finding the cube of a number. For example: Assume ‘y’ as the cube root of 15625, then y3 can be 15625. The cube root of 15625 is an exact value, which is 25.
Finding the Cube Root of 15625
Finding the cube root of a number is to identify the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 15625. The common methods we follow to find the cube root are given below:
- Prime factorization method
- Approximation method
- Subtraction method
- Halley’s method
To find the cube root of a perfect number like 15625, we can use the prime factorization method effectively. Since 15625 is a perfect cube, prime factorization will give us the exact cube root.
Cube Root of 15625 by Prime Factorization Method
Let's find the cube root of 15625 using the prime factorization method.
First, we find the prime factors of 15625:
15625 = 5 × 5 × 5 × 5 × 5 × 5
Grouping the factors in triples, we get: 15625 = (5 × 5 × 5) × (5 × 5 × 5)
Thus, the cube root of 15625 is 5 × 5 = 25.
Common Mistakes and How to Avoid Them in the Cube Root of 15625
Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes students commonly make and the ways to avoid them:
Mistake 1
Trying to find cube roots using approximation for perfect cube numbers.
Students sometimes assume that they would need to approximate the cube root of numbers like 15625, which are perfect cubes. To avoid this error, memorize that some numbers have an exact cube root, such as 15625, which is exactly 25.
Cube Root of 15625 Examples:
Problem 1
Imagine you have a cube-shaped toy that has a total volume of 15625 cubic centimeters. Find the length of one side of the cube equal to its cube root.
Side of the cube = ∛15625 = 25 units
Explanation
To find the side of the cube, we need to find the cube root of the given volume. Therefore, the side length of the cube is exactly 25 units.
Problem 2
A company manufactures 15625 cubic meters of material. Calculate the amount of material left after using 625 cubic meters.
The amount of material left is 15000 cubic meters.
Explanation
To find the remaining material, we need to subtract the used material from the total amount:
15625 - 625 = 15000 cubic meters.
Problem 3
A bottle holds 15625 cubic meters of volume. Another bottle holds a volume of 375 cubic meters. What would be the total volume if the bottles are combined?
The total volume of the combined bottles is 16000 cubic meters.
Explanation
Let’s add the volume of both bottles:
15625 + 375 = 16000 cubic meters.
Problem 4
When the cube root of 15625 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?
2 × 25 = 50
The cube of 50 = 125000
Explanation
When we multiply the cube root of 15625 by 2, it results in a significant increase in the volume because the cube increases exponentially.
Problem 5
Find ∛(4000 + 11625).
∛(4000 + 11625) = ∛15625 = 25
Explanation
As shown in the question ∛(4000 + 11625), we can simplify that by adding them.
So, 4000 + 11625 = 15625.
Then we use this step: ∛15625 = 25 to get the answer.
FAQs on 15625 Cube Root
1.Can we find the Cube Root of 15625?
2.Why is Cube Root of 15625 rational?
3.Is it possible to get the cube root of 15625 as an exact number?
4.Can we find the cube root of any number using prime factorization?
5.Is there any formula to find the cube root of a number?
6.How does learning Algebra help students in Vietnam make better decisions in daily life?
7.How can cultural or local activities in Vietnam support learning Algebra topics such as Cube Root of 15625?
8.How do technology and digital tools in Vietnam support learning Algebra and Cube Root of 15625?
9.Does learning Algebra support future career opportunities for students in Vietnam?
Important Glossaries for Cube Root of 15625
- Cube root: The number that is multiplied three times by itself to get the given number is the cube root of that number.
- Perfect cube: A number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example: 5 × 5 × 5 = 125, therefore, 125 is a perfect cube.
- Exponent: The exponent form of the number denotes the number of times a number is multiplied by itself. In 15625(1/3), ⅓ is the exponent which denotes the cube root of 15625.
- Radical sign: The symbol used to represent a root is expressed as (∛).
- Rational number: A number that can be expressed as a fraction. For example, the cube root of 15625 is rational because it is a whole number.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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